There are plenty of shops along La Ramblas that mainly appeal to tourists, and sell plenty of souvenirs. For a real Spanish experience, take a trip around El Corte Ingles on Place de Catalunya. The equivalent of Harrods, it still offers some good bargains and plenty of choice.
There are plenty of small markets dotted around the city that sell a wide variety of goods, particularly interesting is the antiques market on Placa Nova on Thursdays.
It is worth noting that shops in Barcelona open early - usually around 8.30am, and close for two hours between 11.30am and 1.30pm for Siesta, before reopening until late in the evening.